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Simplifying -16x2 + 208x + 156 = 0 Reorder the terms: 156 + 208x + -16x2 = 0 Solving 156 + 208x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(39 + 52x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(39 + 52x + -4x2)' equal to zero and attempt to solve: Simplifying 39 + 52x + -4x2 = 0 Solving 39 + 52x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -9.75 + -13x + x2 = 0 Move the constant term to the right: Add '9.75' to each side of the equation. -9.75 + -13x + 9.75 + x2 = 0 + 9.75 Reorder the terms: -9.75 + 9.75 + -13x + x2 = 0 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + -13x + x2 = 0 + 9.75 -13x + x2 = 0 + 9.75 Combine like terms: 0 + 9.75 = 9.75 -13x + x2 = 9.75 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 9.75 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 9.75 + 42.25 Combine like terms: 9.75 + 42.25 = 52 42.25 + -13x + x2 = 52 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + -6.5) equal to 7.211102551 and -7.211102551.Subproblem 1
x + -6.5 = 7.211102551 Simplifying x + -6.5 = 7.211102551 Reorder the terms: -6.5 + x = 7.211102551 Solving -6.5 + x = 7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 7.211102551 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 7.211102551 + 6.5 x = 7.211102551 + 6.5 Combine like terms: 7.211102551 + 6.5 = 13.711102551 x = 13.711102551 Simplifying x = 13.711102551Subproblem 2
x + -6.5 = -7.211102551 Simplifying x + -6.5 = -7.211102551 Reorder the terms: -6.5 + x = -7.211102551 Solving -6.5 + x = -7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -7.211102551 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -7.211102551 + 6.5 x = -7.211102551 + 6.5 Combine like terms: -7.211102551 + 6.5 = -0.711102551 x = -0.711102551 Simplifying x = -0.711102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.711102551, -0.711102551}Solution
x = {13.711102551, -0.711102551}
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